1. Agate: an Agda -to- Haskell compiler AIST / CVS Hiroyuki Ozaki (joint work with Makoto Takeyama)

2. What is Agda? Proof assistant based on Martin-Löf type theory. Curry-Howard correspondence available for its core language ⇒ Proof language can be regarded as a functional programming language with dependent types. Full language contains extension of packages, classes (therefore, monads), hidden arguments, metavariables, etc.

3. Goal To provide a tool for experimentation of programming with dependent types. To achieve it, we need –implement the tool quickly –reasonably fast execution of the emitted code –deal with “side effects,” such as I/O.

4. Requirements Treat full Agda language ⇒ use parser of the current Agda implementation Faster execution ⇒ compile, rather than interpret! Quick implementation ⇒ make the target language be Haskell ⇒ Agda language is close to it and there is GHC which generates executable binaries of high quality ⇒ use Higher Order Abstract Syntax ⇒ to eliminate coding for variable substitution

5. Our HOAS Tree data Val = VAbs (Val -> Val) | VCon String [Val] | VStr [(String, Val)] | VIO (IO Val) | VString String apply :: Val -> Val -> Val apply (VAbs f) v = f v select :: Val -> String -> Val select (VStr bs) x = lookup x bs E.g., ( ∖ x -> x) zero ⇨ VAbs ( ∖ x -> x) `apply` (VCon “zero” []) struct { inc = ∖ x -> succ x; n = inc zero } ⇨ let inc = VAbs ( ∖ x -> succ `apply` x) n = inc `apply` zero in VStr [(“n”,n),(“inc”,inc)] Untyped lambda calculus for representing Agda terms

6. How to deal with IO Pass the buck to Haskell! posutulate IO :: Set -> Set posutulate putStr :: String -> IO Unit main :: IO Unit main = putStr “Hello World” data Val = … | VIO (IO Val) | VString String deIO (VIO m) = m deString (VString s) = s x_main, x_putStr :: Val x_main = x_putStr `apply` VString “Hello World” x_putStr = VAbs ( ∖ v -> VIO (putStr (deString v) >> return VUnit )) main :: IO Val main = deIO x_main

7. Performance GHC : Agate = 1 : 6 (execution time) Agda ∞ ∞ ∞ Agate (sec)GHC (sec)ratio fact 80.1300.0225.9 fib 200.0710.0125.9 ack 3 60.1300.0373.5

8. Conclusion Running under Linux, Windows and MacOSX Visit my homepage to download Agate! http://staff.aist.go.jp/hiroyuki.ozaki/ Availability FULL dependently typed functional language including IO, with a very sophisticated development environment